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Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics. It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry.
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The Geometry of Exponential Families. Calculus on Manifolds. Statistical Manifolds. Connections. Curvature. Information Metrices and Statistical Divergences. Asymptotics. Bundles and Tensors. Higher Order Geometry. References. Index.Product Description:
Book by Murray MK Rice JW
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Descrizione libro Chapman and Hall/CRC. Hardcover. Condizione: New. 0412398605 Brand New Book. Codice articolo 48505
Descrizione libro Chapman and Hall/CRC, 1993. HRD. Condizione: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice articolo F9-9780412398605
Descrizione libro Chapman and Hall/CRC, 1993. Condizione: New. book. Codice articolo M0412398605
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Descrizione libro Chapman & Hall, 1993. Hardcover. Condizione: Brand New. 1st edition. 288 pages. 9.00x5.50x0.75 inches. In Stock. Codice articolo __0412398605
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Descrizione libro Chapman and Hall/CRC, 1993. Hardcover. Condizione: New. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. Buy with confidence, excellent customer service! Softcover reprint of the original 1st ed. 1993. Codice articolo 0412398605n